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Bayesian Methods applied to Reflection Seismology

Abstract

Quantifying uncertainty in models derived from observed seismic data is an important issue in exploration geophysics. In this research we examine the geological structure of the subsurface of the Earth using controlled source seismology which consists of data recorded in time and the distance between acoustic sources and receivers. There are a number of inversion tools to map data into depth models, but a full exploration of the uncertainty of such models is rarely done because of the lack of robust strategies available for the analysis of large non-linear complex systems.

In reflection seismology, there are three principal sources of uncertainty: the first comes from the input data which is noisy and band-limited, the second is from the modeling assumptions used to approximate the physics of the problem in order to make the problem tractable, and the last is from the ambiguity in data and model selection. The latter is by far the hardest source of uncertainty to assess, not only are there a large number of models which are appropriate for a given seismic profile and still physically and geologically plausible, but also the judgement related to the acceptability of a model varies according to the expert handling the data. The fact that there are many possible solutions, depending on how the problem is treated, adds a new layer of uncertainty to the question.

Here we propose a Bayesian approach to assess the uncertainty in velocity models derived from seismic reflection data. We have developed a method used to identify and track seismic events called the Seismic Event Tracking algorithm. We then created the BRAINS (Bayesian Regression Analysis in Seismology) class of models used to estimate velocities, travel times and depths with associated measures of uncertainty for each identified horizon. Since the experts' prior judgements and problem requirements vary according to the situation being analysed, the Bayesian methodology is the most appropriate to create a gray box that accepts the input of prior knowledge but that is also able to cope with vague or no prior information; here each model in the BRAINS class can be used at different stages of seismic processing, depending on the inputs necessary for the next step of modeling. Moreover, each estimate produced has an uncertainty model attached that can be explored before making a decision.

In order to investigate the robustness of the models proposed, we analysed a series of single and multigathered synthetic examples, some of which had attributes that differ from the modeling assumptions or carried ambiguities derived from the limitations of data recording. Finally, we analysed a 2D real data set part of a seismic survey acquired over the Naturaliste Plateau and Mentelle Basins off the south west coast of Australia. We show the efficiency of the BRAINS approach on real data and recover velocity and depth models with posterior depth standard errors of at most 0.4% relative to posterior depth means, and posterior RMS velocity standard errors of at most 1.7% relative of posterior RMS velocity means. We also observe that variations in interval velocities is higher with an average of 2.4% for the posterior interval velocity standard deviation and mean ratio which reaches a maximum of 23.7% in areas of high uncertainty.